Yes.
It's that simple. The general rule applies. Since your home state (FL) does not have an income tax, there will be no resident state credit. Any amount of VA source income dictates a filing requirement.
The general rule is: your report all your income on your home state return, even the income earned out of state. You file a non-resident state return for the state you worked in or otherwise had income sourced in (e.g. sale of property located in that state) and pay tax to that state. Your home state will give you a credit, or partial credit, for what you paid the non-resident state.
For state filing requirements, VA, like most states, does not, go by what you earned in their state but by your total income . For example, VA has a $11,950 ($23,900 Married filing jointly) filing requirement. If your total income for the year was $15,000; you would be required to file even though you may have had only $300 of income in VA. But if your total income was $9,000 you would not need to file.